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<title>Tolerances</TITLE>
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<H2> SDSS 2.5 M COLLIMATION SENSITIVITY STUDY</H2>
<CENTER>Prepared 9/17/97</center>
<center>Steve Kent</center>
<P>
The following table gives the sensitivity of field center, distortion, and
image size to various misalignments of the optical elements in the 2.5 m
telescope.
Only the spectroscopic mode is examined here (the results are comparable for
imaging mode).
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Vital information:  All calculations are done for a monochromatic image
at about 0.48 micron wavelength.  The original spectroscopic design is
tweaked in only one way: the secondary is refocused for a single wavelength;
in the original design, focus was done for a polychromatic image.
Each row in the following table corresponds to decollimation of a single
degree of freedom followed by a refocus and a "repointing" of the telescope.
The repointing is done so as to keep the center of the focal plane
pointed to the same position on the sky.
(In a previous analysis, I had allowed the focal plane to translate -
this is not what happens in reality at the mountain, and leads to an
erroneous calcuation of distortion errors).
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The performance criteria that I use are all calculated for images in the focal
plane.  The quantities that I measure are:
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<DIR>
<LI>1. Field shift (this is the mean shift in object positions in the focal
plane before repointing the telescope)
<LI>2. Distortion  (residual object position shift after repointing)
<LI>3,4. Increase in FWHM in two directions (this is computed by subtracting the
     new FWHM from the old FWHM in quadrature).
</dir>
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Image properties are measured for an array of points in the focal plane.
The numbers entered in the table are the worst case changes across the
array.  Typically, these occur for objects
on the periphery of the field of view.
I use a focal plane with a radius of 327 mm.
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All image parameters in the following table are in units of microns.
The units for the decollimation steps are given.

<PRE>
						-INCREMENTAL-
Optic	Motion	Amount	Unit	Field	Distor-	FWHM X	FWHM Y
				shift	tion		
				------------microns-----------
Spectroscopic Mode					
							
M1	Offset	1	mm	2183	0	61	50
M1	Tilt	1	'	7210	1	86	74
M2	Offset	1	mm	1185	6	64	49
M2	Tilt	1	'	2545	3	65	31
C1	Offset	1	mm	16	32	40	42
C2	Offset	1	mm	12	15	0	0
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